Background

This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): biomass productivity trend, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selects the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).

model 1: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 2: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)

Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Two Log-normal models are fitted: 1) the simple model, and 2) the \(\alpha\) model: account for growth compensation due to plot biomass loss.

model 4: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 5: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6880     1758.3                                
## 2   6879     1588.0  1 170.38  738.11 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 74579.98
## 2     2 73880.45
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.69176    0.17752   3.897 9.84e-05 ***
## alpha   0.83853    0.02819  29.742  < 2e-16 ***
## A     416.54207   27.03681  15.406  < 2e-16 ***
## k     188.16891   13.29611  14.152  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4805 on 6879 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.098e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   6879     1588.0                          
## 2   6878     1587.8  1 0.10967   0.475 0.4907
##   model      AIC
## 1     2 73880.45
## 2    2a 73881.97
## 3    2b 73864.22
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.64525    0.17419   3.704 0.000214 ***
## alpha   0.84366    0.02836  29.752  < 2e-16 ***
## A     267.35244   24.48232  10.920  < 2e-16 ***
## k      87.16041   11.89186   7.329 2.58e-13 ***
## s       1.22609    0.05764  21.273  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4799 on 6878 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.167e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6878     1726.3                                
## 2   6877     1557.0  1 169.29  747.71 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 73864.22
## 2     3 74457.48
## 3     4 73749.07
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.81288    0.18481   4.398 1.11e-05 ***
## alpha   0.83154    0.02775  29.971  < 2e-16 ***
## a      31.22968    1.70998  18.263  < 2e-16 ***
## b     112.93234    5.39611  20.928  < 2e-16 ***
## c     123.66007    5.88096  21.027  < 2e-16 ***
## d       1.06739    0.04852  21.999  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4758 on 6877 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  21456     6780.2                                
## 2  21455     6542.2  1 237.98  780.44 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 223452.5
## 2     2 222687.8
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95393    0.10285   9.275   <2e-16 ***
## alpha   0.76407    0.02559  29.853   <2e-16 ***
## A     167.63507    4.38459  38.233   <2e-16 ***
## k      78.56108    2.47525  31.739   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5522 on 21455 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.327e-06
##   (1226 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  21455     6542.2                                
## 2  21454     6515.0  1 27.151  89.409 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 222687.8
## 2    2a 222600.5
## 3    2b 222539.7
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.06559    0.10698   9.961   <2e-16 ***
## alpha   0.76996    0.02564  30.034   <2e-16 ***
## A     115.78050    3.70206  31.275   <2e-16 ***
## k      40.57330    1.64862  24.610   <2e-16 ***
## s       1.41290    0.04066  34.748   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5503 on 21454 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 4.417e-06
##   (1226 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  21454     6676.2                                
## 2  21453     6430.8  1 245.39  818.61 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 222539.7
## 2     3 223124.9
## 3     4 222323.3
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.07103    0.10677   10.03   <2e-16 ***
## alpha   0.77321    0.02528   30.59   <2e-16 ***
## a      22.95843    0.83356   27.54   <2e-16 ***
## b      67.52314    1.55360   43.46   <2e-16 ***
## c     103.10031    2.16612   47.60   <2e-16 ***
## d       1.08732    0.02951   36.85   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5475 on 21453 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1226 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6934    1078.14                                
## 2   6933     950.93  1 127.21  927.46 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 75745.30
## 2     2 74876.34
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.16754    0.11201   1.496    0.135    
## alpha   0.88651    0.02699  32.844   <2e-16 ***
## A     438.44852   23.33717  18.788   <2e-16 ***
## k     125.86939    8.34455  15.084   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3704 on 6933 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.061e-06
##   (370 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6933     950.93                                
## 2   6932     944.77  1 6.1579  45.182 1.938e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 74876.34
## 2    2a 74833.27
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.19985    0.11340   1.762  0.07805 .  
## alpha   0.88716    0.02706  32.787  < 2e-16 ***
## A     297.82149   16.82169  17.705  < 2e-16 ***
## k      36.53118    7.80982   4.678 2.96e-06 ***
## p      -0.36908    0.11916  -3.097  0.00196 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3692 on 6932 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.535e-06
##   (370 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6932    1067.83                                
## 2   6931     941.94  1 125.89  926.36 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 74833.27
## 2     3 75682.64
## 3     4 74814.41
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.19868    0.11312   1.756   0.0791 .  
## alpha   0.88629    0.02701  32.817  < 2e-16 ***
## a      46.50096   10.46650   4.443 9.02e-06 ***
## b     143.42164   12.84562  11.165  < 2e-16 ***
## c     119.23589    8.07145  14.773  < 2e-16 ***
## d       1.10698    0.12085   9.160  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3686 on 6931 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (370 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5547     1704.0                                
## 2   5546     1616.1  1 87.972   301.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 59908.34
## 2     2 59616.16
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.97722    0.20650   4.732 2.28e-06 ***
## alpha   0.83417    0.04432  18.822  < 2e-16 ***
## A     365.92255   32.26558  11.341  < 2e-16 ***
## k     190.74942   19.15547   9.958  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5398 on 5546 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.557e-06
##   (296 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5546     1616.1                                
## 2   5545     1585.5  1 30.557  106.87 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 59616.16
## 2    2a 59512.21
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.06896    0.21114   5.063 4.26e-07 ***
## alpha   0.86162    0.04368  19.726  < 2e-16 ***
## A     194.67994   12.87743  15.118  < 2e-16 ***
## k      40.40127    6.99591   5.775 8.11e-09 ***
## p      -0.33156    0.07736  -4.286 1.85e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5347 on 5545 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.118e-06
##   (296 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5545     1667.1                                
## 2   5544     1570.6  1 96.455  340.47 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 59512.21
## 2     3 59790.56
## 3     4 59461.77
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.06254    0.20963   5.069 4.14e-07 ***
## alpha   0.87213    0.04334  20.125  < 2e-16 ***
## a      19.41594    3.70394   5.242 1.65e-07 ***
## b      96.66094    5.38215  17.960  < 2e-16 ***
## c     101.25661    4.50967  22.453  < 2e-16 ***
## d       1.02471    0.07125  14.382  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5323 on 5544 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (296 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9432     1587.5                                
## 2   9431     1471.4  1 116.06  743.86 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 98445.42
## 2     2 97731.13
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.9572     0.1106   8.651   <2e-16 ***
## alpha   0.7909     0.0270  29.288   <2e-16 ***
## A     179.3531     5.9484  30.152   <2e-16 ***
## k      52.8587     2.8565  18.505   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.395 on 9431 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.096e-07
##   (571 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9431     1471.4                                
## 2   9430     1465.8  1 5.5843  35.925 2.126e-09 ***
## 3   9430     1465.3  0 0.0000                      
## 4   9429     1465.2  1 0.0872   0.561    0.4539    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 97731.13
## 2    2a 97697.26
## 3    2b 97693.91
## 4    2c 97695.35
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.96491    0.11082   8.707   <2e-16 ***
## alpha   0.79208    0.02697  29.372   <2e-16 ***
## A     128.12523    4.67964  27.379   <2e-16 ***
## k      32.43433    0.96401  33.645   <2e-16 ***
## s       1.85487    0.14913  12.438   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3942 on 9430 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.503e-06
##   (571 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9430     1580.5                                
## 2   9429     1464.6  1 115.85  745.85 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 97693.91
## 2     3 98407.53
## 3     4 97691.25
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "223", :
## provided 32 variables to replace 31 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95467    0.11054   8.637  < 2e-16 ***
## alpha   0.79131    0.02698  29.328  < 2e-16 ***
## a      14.36005   24.74403   0.580    0.562    
## b     100.63809   25.72856   3.912 9.24e-05 ***
## c     118.73960   12.04638   9.857  < 2e-16 ***
## d       1.55264    0.35970   4.316 1.60e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3941 on 9429 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (571 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12112     2738.8                                
## 2  12111     2512.1  1 226.69  1092.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 130399.6
## 2     2 129354.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.31050    0.12159   10.78   <2e-16 ***
## alpha   0.71119    0.01999   35.59   <2e-16 ***
## A     278.85285    8.36741   33.33   <2e-16 ***
## k      76.76299    2.35893   32.54   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4554 on 12111 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.78e-06
##   (729 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1  12111     2512.1                               
## 2  12110     2485.7  1 26.3813 128.5253 <2e-16 ***
## 3  12109     2485.6  1  0.0694   0.3383 0.5608    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 129354.9
## 2    2a 129229.0
## 3    2b       NA
## 4    2c 129230.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     1.296348   0.120428  10.765   <2e-16 ***
## alpha   0.718309   0.020363  35.275   <2e-16 ***
## A     220.176569   6.649464  33.112   <2e-16 ***
## k      42.722737   2.304084  18.542   <2e-16 ***
## p      -0.062849   0.007588  -8.283   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4531 on 12110 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.038e-06
##   (729 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12110     2709.7                                
## 2  12109     2486.7  1 223.02    1086 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 129229.0
## 2     3 130274.4
## 3     4 129235.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     1.296348   0.120428  10.765   <2e-16 ***
## alpha   0.718309   0.020363  35.275   <2e-16 ***
## A     220.176569   6.649464  33.112   <2e-16 ***
## k      42.722737   2.304084  18.542   <2e-16 ***
## p      -0.062849   0.007588  -8.283   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4531 on 12110 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.038e-06
##   (729 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12427     4751.2                                
## 2  12426     4496.0  1 255.23  705.42 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 137630.1
## 2     2 136945.7
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.79958    0.13463   5.939 2.94e-09 ***
## alpha   0.66173    0.02305  28.704  < 2e-16 ***
## A     296.34997   11.52223  25.720  < 2e-16 ***
## k      81.84131    3.24704  25.205  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6015 on 12426 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.623e-06
##   (737 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  12426     4496.0                                 
## 2  12425     4481.7  1 14.2985 39.6414 3.154e-10 ***
## 3  12425     4479.1  0  0.0000                      
## 4  12424     4479.0  1  0.1142  0.3168    0.5735    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 136945.7
## 2    2a 136908.1
## 3    2b 136901.1
## 4    2c 136902.8
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.79154    0.13392   5.911  3.5e-09 ***
## alpha   0.67002    0.02357  28.426  < 2e-16 ***
## A     206.16286    9.61009  21.453  < 2e-16 ***
## k      41.26733    2.85865  14.436  < 2e-16 ***
## s       1.22628    0.03283  37.347  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6004 on 12425 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.442e-06
##   (737 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12425     4726.6                                
## 2  12424     4479.2  1 247.46  686.39 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 136901.1
## 2     3 137569.6
## 3     4 136903.2
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.79154    0.13392   5.911  3.5e-09 ***
## alpha   0.67002    0.02357  28.426  < 2e-16 ***
## A     206.16286    9.61009  21.453  < 2e-16 ***
## k      41.26733    2.85865  14.436  < 2e-16 ***
## s       1.22628    0.03283  37.347  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6004 on 12425 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.442e-06
##   (737 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

234 - lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1273     342.72                                
## 2   1272     305.18  1 37.541  156.47 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14240.14
## 2     2 14094.10
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52561    0.40921   1.284    0.199    
## alpha   0.79999    0.05788  13.821  < 2e-16 ***
## A     478.26877   81.98228   5.834 6.86e-09 ***
## k     153.20836   30.69689   4.991 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 1272 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.326e-06
##   (68 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1272     305.18                          
## 2   1271     304.82  1 0.35578  1.4835 0.2235
##   model      AIC
## 1     2 14094.10
## 2    2a 14094.62
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52561    0.40921   1.284    0.199    
## alpha   0.79999    0.05788  13.821  < 2e-16 ***
## A     478.26877   81.98228   5.834 6.86e-09 ***
## k     153.20836   30.69689   4.991 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 1272 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.326e-06
##   (68 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Error in nls(f_3, data = G_234, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     2 14094.10
## 2     3       NA
## 3     4 14096.77
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52561    0.40921   1.284    0.199    
## alpha   0.79999    0.05788  13.821  < 2e-16 ***
## A     478.26877   81.98228   5.834 6.86e-09 ***
## k     153.20836   30.69689   4.991 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 1272 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.326e-06
##   (68 observations deleted due to missingness)

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: fits

predict and plot

`## plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2165     468.74                                
## 2   2164     449.79  1 18.948   91.16 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 22573.55
## 2     2 22486.10
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.30617    0.21270   1.439     0.15    
## alpha   0.70921    0.06963  10.186   <2e-16 ***
## A     234.25380   19.13609  12.241   <2e-16 ***
## k      86.34944    9.58196   9.012   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4559 on 2164 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.498e-06
##   (122 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2164     449.79                                
## 2   2163     442.07  1 7.7182  37.764 9.477e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 22486.10
## 2    2a 22450.57
## 3    2b 22453.39
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.40256    0.21862   1.841   0.0657 .  
## alpha   0.71553    0.06967  10.270   <2e-16 ***
## A     148.57344   10.23035  14.523   <2e-16 ***
## k       5.24468    5.41531   0.968   0.3329    
## p      -3.23715    3.60610  -0.898   0.3695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4521 on 2163 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 8.969e-06
##   (122 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2163     462.14                                
## 2   2162     443.26  1 18.877  92.069 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 22450.57
## 2     3 22546.83
## 3     4 22458.41
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.40256    0.21862   1.841   0.0657 .  
## alpha   0.71553    0.06967  10.270   <2e-16 ***
## A     148.57344   10.23035  14.523   <2e-16 ***
## k       5.24468    5.41531   0.968   0.3329    
## p      -3.23715    3.60610  -0.898   0.3695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4521 on 2163 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 8.969e-06
##   (122 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    708     336.70                                
## 2    707     329.96  1 6.7436  14.449 0.0001564 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7311.058
## 2     2 7298.673
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2620     0.4735  -0.553  0.58018    
## alpha   0.4666     0.1144   4.077 5.07e-05 ***
## A     317.9208    75.0171   4.238 2.55e-05 ***
## k     133.3036    34.6376   3.849  0.00013 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6832 on 707 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.037e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    707     329.96                          
## 2    706     329.85  1 0.10851  0.2322   0.63
##   model      AIC
## 1     2 7298.673
## 2    2a 7300.439
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2620     0.4735  -0.553  0.58018    
## alpha   0.4666     0.1144   4.077 5.07e-05 ***
## A     317.9208    75.0171   4.238 2.55e-05 ***
## k     133.3036    34.6376   3.849  0.00013 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6832 on 707 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.037e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    706     321.06                                
## 2    705     310.62  1 10.448  23.714 1.381e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 7298.673
## 2     3 7281.242
## 3     4 7259.720
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.3313     0.4397  -0.754    0.451    
## alpha   0.5608     0.1051   5.333 1.30e-07 ***
## a      11.8038     1.9008   6.210 9.06e-10 ***
## b      88.9590    10.2328   8.693  < 2e-16 ***
## c      58.2985     5.0380  11.572  < 2e-16 ***
## d       1.0553     0.0947  11.143  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6638 on 705 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    155     28.883                              
## 2    154     27.554  1 1.3296  7.4314 0.007153 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1995.769
## 2     2 1990.323
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## tau      1.2518     2.1470   0.583  0.56070   
## alpha    0.7269     0.2520   2.885  0.00448 **
## A     5419.6547  2776.6065   1.952  0.05276 . 
## k     1453.0069   510.1242   2.848  0.00500 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.423 on 154 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 4.387e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    154     27.554                             
## 2    153     26.681  1 0.87281  5.0051 0.02672 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 1990.323
## 2    2a 1987.237
## 3    2b       NA
## 4    2c       NA
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.752e+00  2.562e+00   0.684 0.495280    
## alpha 8.326e-01  2.442e-01   3.410 0.000831 ***
## A     1.590e+04  2.006e+04   0.793 0.429275    
## k     5.997e+03  7.916e+03   0.758 0.449878    
## p     2.363e-03  2.414e-03   0.979 0.329190    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4176 on 153 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.066e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    153     30.979                             
## 2    152     29.287  1 1.6923  8.7832 0.00353 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 1987.237
## 2     3 2010.835
## 3     4 2003.960
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.752e+00  2.562e+00   0.684 0.495280    
## alpha 8.326e-01  2.442e-01   3.410 0.000831 ***
## A     1.590e+04  2.006e+04   0.793 0.429275    
## k     5.997e+03  7.916e+03   0.758 0.449878    
## p     2.363e-03  2.414e-03   0.979 0.329190    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4176 on 153 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.066e-06
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    214     67.657                           
## 2    213     67.621  1 0.036228  0.1141 0.7358
##   model      AIC
## 1     1 2322.942
## 2     2 2324.826
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## tau  -0.8160     0.9509  -0.858   0.3918  
## A   277.8964   110.6751   2.511   0.0128 *
## k   159.0901    64.0178   2.485   0.0137 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5623 on 214 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.666e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    214     67.657                          
## 2    213     67.505  1 0.15278  0.4821 0.4882
##   model      AIC
## 1     1 2322.942
## 2    1a 2324.452
## 3    1b       NA
## 4    1c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## tau  -0.8160     0.9509  -0.858   0.3918  
## A   277.8964   110.6751   2.511   0.0128 *
## k   159.0901    64.0178   2.485   0.0137 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5623 on 214 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.666e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    212     62.692                          
## 2    211     62.465  1 0.22643  0.7649 0.3828
##   model      AIC
## 1     1 2322.942
## 2     3 2310.402
## 3     4 2311.616
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## tau  -1.45035    0.59364  -2.443 0.015377 *  
## a    40.15842   12.25407   3.277 0.001225 ** 
## b   148.91132   39.27593   3.791 0.000195 ***
## c   142.76710    8.69554  16.418  < 2e-16 ***
## d     0.64093    0.09421   6.803 1.03e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5438 on 212 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in nls(f_1, data = G_322, start = c(tau = tau.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

332 - Great Plains Steppe

  • Cannot fit model

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    205     109.38                            
## 2    204     107.28  1 2.0903  3.9748 0.04752 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2230.704
## 2     2 2228.690
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.4762     1.5880   0.300    0.765  
## alpha   0.6443     0.2929   2.200    0.029 *
## A     502.5964   606.4813   0.829    0.408  
## k     360.7593   468.4009   0.770    0.442  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7252 on 204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.93e-06
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model     AIC
## 1     2 2228.69
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.4762     1.5880   0.300    0.765  
## alpha   0.6443     0.2929   2.200    0.029 *
## A     502.5964   606.4813   0.829    0.408  
## k     360.7593   468.4009   0.770    0.442  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7252 on 204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.93e-06
##   (24 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Error in nls(f_3, data = G_332, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_4, data = G_332, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model     AIC
## 1     2 2228.69
## 2     3      NA
## 3     4      NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.4762     1.5880   0.300    0.765  
## alpha   0.6443     0.2929   2.200    0.029 *
## A     502.5964   606.4813   0.829    0.408  
## k     360.7593   468.4009   0.770    0.442  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7252 on 204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.93e-06
##   (24 observations deleted due to missingness)

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit

  • log-normal alpha model: does not fit

  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6772     1333.1                                
## 2   6771     1152.4  1 180.72  1061.8 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71776.53
## 2     2 70791.58
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.83471    0.16884   4.944 7.84e-07 ***
## alpha   0.80612    0.02248  35.855  < 2e-16 ***
## A     416.13390   24.57826  16.931  < 2e-16 ***
## k     192.41525   11.49858  16.734  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4125 on 6771 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.492e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6771     1152.4                                
## 2   6770     1144.3  1 8.0931  47.881 4.944e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 70791.58
## 2    2a 70745.83
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     0.720852   0.161462   4.465 8.15e-06 ***
## alpha   0.814665   0.022641  35.982  < 2e-16 ***
## A     311.623953  18.279896  17.047  < 2e-16 ***
## k     106.277700  10.003747  10.624  < 2e-16 ***
## p      -0.044463   0.009478  -4.691 2.77e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4111 on 6770 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.248e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6770     1322.9                                
## 2   6769     1140.1  1 182.86  1085.7 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 70745.83
## 2     3 71728.53
## 3     4 70722.69
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.72103    0.16125   4.471 7.90e-06 ***
## alpha   0.81660    0.02244  36.392  < 2e-16 ***
## a      11.86910    2.87240   4.132 3.64e-05 ***
## b     156.98730   10.86890  14.444  < 2e-16 ***
## c     207.69052   26.59499   7.809 6.62e-15 ***
## d       1.72266    0.11349  15.179  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4104 on 6769 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7751     1167.8                                
## 2   7750     1080.3  1 87.472  627.52 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85843.11
## 2     2 85241.40
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.91183    0.12119   7.524 5.91e-14 ***
## alpha   0.90018    0.03388  26.571  < 2e-16 ***
## A     223.88494    7.41504  30.193  < 2e-16 ***
## k      43.44403    2.42381  17.924  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3734 on 7750 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.246e-06
##   (432 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7750     1080.3                                
## 2   7748     1066.6  2 13.731  49.874 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 85241.40
## 2    2a       NA
## 3    2b 85154.38
## 4    2c 85146.21
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.99857    0.12481   8.001 1.41e-15 ***
## alpha   0.89771    0.03372  26.622  < 2e-16 ***
## A     154.79938    4.49176  34.463  < 2e-16 ***
## k      44.43699    2.39761  18.534  < 2e-16 ***
## p       0.40664    0.05999   6.779 1.30e-11 ***
## s       3.75774    0.53787   6.986 3.06e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.371 on 7748 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 9.783e-06
##   (432 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7749     1151.2                                
## 2   7748     1064.1  1 87.036  633.71 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 85146.21
## 2     3 85736.15
## 3     4 85128.55
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.99348    0.12427   7.994 1.49e-15 ***
## alpha   0.89846    0.03365  26.700  < 2e-16 ***
## a      49.42999   12.68864   3.896 9.88e-05 ***
## b     102.10729   12.62474   8.088 6.99e-16 ***
## c     100.61164    3.18931  31.547  < 2e-16 ***
## d       1.10537    0.12889   8.576  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3706 on 7748 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (432 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     122.26                                
## 2    886     106.68  1 15.583  129.42 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9055.244
## 2     2 8935.898
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.01094    0.25540  -0.043    0.966    
## alpha   0.89519    0.07261  12.329  < 2e-16 ***
## A     292.54555   34.23433   8.545  < 2e-16 ***
## k      95.82504   15.20296   6.303  4.6e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.347 on 886 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.455e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    886     106.68                             
## 2    885     106.00  1 0.67604  5.6442 0.01773 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 8935.898
## 2    2a 8932.240
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.04774    0.26180   0.182   0.8553    
## alpha   0.90336    0.07277  12.413  < 2e-16 ***
## A     225.89814   25.25934   8.943  < 2e-16 ***
## k      51.43265   12.26266   4.194 3.01e-05 ***
## p      -0.08665    0.04437  -1.953   0.0512 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3461 on 885 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.431e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    885     121.92                                
## 2    884     106.29  1 15.629  129.98 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 8932.240
## 2     3 9056.791
## 3     4 8936.700
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.04774    0.26180   0.182   0.8553    
## alpha   0.90336    0.07277  12.413  < 2e-16 ***
## A     225.89814   25.25934   8.943  < 2e-16 ***
## k      51.43265   12.26266   4.194 3.01e-05 ***
## p      -0.08665    0.04437  -1.953   0.0512 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3461 on 885 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.431e-06
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    955     204.76                                
## 2    954     190.05  1 14.711  73.843 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9951.187
## 2     2 9881.765
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.46206    0.43464   1.063    0.288    
## alpha   0.77623    0.08421   9.218  < 2e-16 ***
## A     306.46634   52.06959   5.886 5.48e-09 ***
## k     133.47106   25.97517   5.138 3.36e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4463 on 954 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.065e-06
##   (51 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    954     190.05                          
## 2    953     189.87  1 0.18837  0.9455 0.3311
##   model      AIC
## 1     2 9881.765
## 2    2a 9882.815
## 3    2b 9883.524
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.46206    0.43464   1.063    0.288    
## alpha   0.77623    0.08421   9.218  < 2e-16 ***
## A     306.46634   52.06959   5.886 5.48e-09 ***
## k     133.47106   25.97517   5.138 3.36e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4463 on 954 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.065e-06
##   (51 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Error in nls(f_4, data = G_M231, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     2 9881.765
## 2     3 9954.667
## 3     4       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.46206    0.43464   1.063    0.288    
## alpha   0.77623    0.08421   9.218  < 2e-16 ***
## A     306.46634   52.06959   5.886 5.48e-09 ***
## k     133.47106   25.97517   5.138 3.36e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4463 on 954 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.065e-06
##   (51 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: does not fit

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3298     2133.7                                
## 2   3297     2025.3  1 108.38  176.43 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 43707.67
## 2     2 43537.59
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   5.191e-01  6.682e-01   0.777    0.437    
## alpha 1.013e+00  6.953e-02  14.570  < 2e-16 ***
## A     1.011e+03  1.753e+02   5.765 8.94e-09 ***
## k     3.764e+02  3.589e+01  10.485  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7838 on 3297 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.623e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3297     2025.3                                
## 2   3296     1977.6  1 47.753  79.588 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 43537.59
## 2    2a 43460.83
## 3    2b 43454.65
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.53718    0.65998   0.814    0.416    
## alpha   1.07143    0.06934  15.451  < 2e-16 ***
## A     536.31143   86.55496   6.196  6.5e-10 ***
## k     119.02407   10.27404  11.585  < 2e-16 ***
## s       1.45921    0.05940  24.566  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7739 on 3296 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.462e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3296     2088.0                                
## 2   3295     1970.6  1  117.4   196.3 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 43454.65
## 2     3 43640.14
## 3     4 43451.11
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5901     0.6749   0.874    0.382    
## alpha   1.0753     0.0695  15.472  < 2e-16 ***
## a       0.0000     5.4149   0.000    1.000    
## b     467.6358    77.2386   6.054 1.57e-09 ***
## c     581.4147   102.1728   5.691 1.38e-08 ***
## d       2.0957     0.1343  15.603  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7733 on 3295 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1983     1184.8                                
## 2   1982     1168.9  1 15.894   26.95 2.302e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24895.19
## 2     2 24870.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     7.8534     4.3636   1.800  0.07205 .  
## alpha   0.6133     0.1100   5.576 2.80e-08 ***
## A     145.3203    54.2373   2.679  0.00744 ** 
## k     128.1086    16.9324   7.566 5.86e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.768 on 1982 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.423e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   1982     1168.9                            
## 2   1981     1166.8  1 2.1673  3.6797 0.05522 .
## 3   1981     1168.2  0 0.0000                  
## 4   1980     1166.2  1 2.0169  3.4243 0.06439 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 24870.37
## 2    2a 24868.68
## 3    2b 24871.21
## 4    2c 24869.78
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     7.87846    4.37803   1.800  0.07208 .  
## alpha   0.62355    0.11083   5.626 2.10e-08 ***
## A     130.60786   48.82237   2.675  0.00753 ** 
## k      90.96584   18.25938   4.982 6.84e-07 ***
## p      -0.06446    0.03772  -1.709  0.08758 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7674 on 1981 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.152e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   1981     1182.3                               
## 2   1980     1166.2  1 16.138    27.4 1.83e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 24868.68
## 2     3 24894.97
## 3     4 24869.67
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     7.87846    4.37803   1.800  0.07208 .  
## alpha   0.62355    0.11083   5.626 2.10e-08 ***
## A     130.60786   48.82237   2.675  0.00753 ** 
## k      90.96584   18.25938   4.982 6.84e-07 ***
## p      -0.06446    0.03772  -1.709  0.08758 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7674 on 1981 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.152e-06
##   (7 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit

  • log-normal alpha model: does not fit

  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    363     122.71                                
## 2    362     118.32  1 4.3863  13.419 0.0002862 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3833.912
## 2     2 3822.590
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.9293     0.3039  -6.349 6.49e-10 ***
## alpha   0.5582     0.1420   3.930 0.000102 ***
## A     574.0776   210.6322   2.725 0.006732 ** 
## k     232.2820   111.8287   2.077 0.038495 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5717 on 362 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.569e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1    362     118.32                           
## 2    361     116.79  1 1.5355  4.7465   0.03 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3822.590
## 2    2a 3819.809
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     -1.94798    0.29564  -6.589 1.57e-10 ***
## alpha    0.59640    0.13334   4.473 1.04e-05 ***
## A     1027.37948  910.11547   1.129    0.260    
## k      568.28926  621.17133   0.915    0.361    
## p        0.02248    0.01655   1.358    0.175    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5688 on 361 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.979e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    361     120.72                                
## 2    360     115.26  1 5.4536  17.034 4.567e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 3819.809
## 2     3 3831.912
## 3     4 3816.992
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables
## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.8271     0.3338  -5.473 8.29e-08 ***
## alpha   0.6108     0.1286   4.749 2.96e-06 ***
## a      42.6892    11.0490   3.864 0.000132 ***
## b     180.7375    41.0611   4.402 1.42e-05 ***
## c     177.7659    40.8862   4.348 1.79e-05 ***
## d       0.9807     0.2073   4.730 3.23e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5658 on 360 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1736     651.22                                
## 2   1735     600.64  1 50.579   146.1 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18138.23
## 2     2 17999.63
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.85360    0.35023  -2.437   0.0149 *  
## alpha   0.59310    0.04314  13.747  < 2e-16 ***
## A     274.07835   36.52316   7.504 9.82e-14 ***
## k     131.06768   13.53831   9.681  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 1735 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.714e-06
##   (18 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'tau', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model
## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 +  : 
##   variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   1735     600.64                            
## 2   1734     598.66  1 1.9884  5.7594 0.01651 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 17999.63
## 2    2a 17995.87
## 3    2b 18000.53
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau    -0.851806   0.350036  -2.433  0.01505 *  
## alpha   0.596415   0.042420  14.060  < 2e-16 ***
## A     313.504594  50.186713   6.247 5.26e-10 ***
## k     179.346930  35.549874   5.045 5.01e-07 ***
## p       0.024058   0.008757   2.747  0.00607 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5876 on 1734 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.467e-06
##   (18 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1734     645.18                                
## 2   1733     592.96  1 52.222  152.63 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 17995.87
## 2     3 18126.02
## 3     4 17981.24
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.87412    0.34288  -2.549   0.0109 *  
## alpha   0.59872    0.04208  14.227  < 2e-16 ***
## a      27.03865    4.19436   6.446 1.48e-10 ***
## b     136.75568   18.11257   7.550 6.98e-14 ***
## c     241.17341   35.91839   6.714 2.55e-11 ***
## d       1.48402    0.13904  10.673  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5849 on 1733 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (18 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2617     1396.7                                
## 2   2616     1367.2  1 29.553  56.548 7.493e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28732.83
## 2     2 28678.80
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.7345     0.8110   0.906    0.365    
## alpha   0.4532     0.0565   8.021 1.56e-15 ***
## A     213.4846    40.2569   5.303 1.23e-07 ***
## k     149.0161    14.4932  10.282  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7229 on 2616 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.067e-06
##   (1 observation deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   2616     1367.2                                 
## 2   2615     1366.1  1  1.0599  2.0289    0.1545    
## 3   2615     1366.8  0  0.0000                      
## 4   2614     1351.0  1 15.7949 30.5617 3.554e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 28678.80
## 2    2a 28678.77
## 3    2b 28680.04
## 4    2c 28651.58
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.83577    0.84704   0.987    0.324    
## alpha   0.45196    0.05499   8.218 3.21e-16 ***
## A     133.15226   26.79988   4.968 7.19e-07 ***
## k      75.15432    7.52220   9.991  < 2e-16 ***
## p       0.07982    0.01467   5.442 5.75e-08 ***
## s       1.75902    0.17763   9.903  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7189 on 2614 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.142e-06
##   (1 observation deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2615     1381.0                                
## 2   2614     1348.8  1 32.212   62.43 4.031e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 28651.58
## 2     3 28707.13
## 3     4 28647.29
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.84900    0.84964   0.999    0.318    
## alpha   0.45685    0.05461   8.365  < 2e-16 ***
## a      11.69323    2.46329   4.747 2.18e-06 ***
## b     104.61495   20.34549   5.142 2.92e-07 ***
## c     258.30931   37.51848   6.885 7.22e-12 ***
## d       1.65652    0.12460  13.294  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7183 on 2614 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1753     893.12                                
## 2   1752     852.89  1 40.224  82.628 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19820.05
## 2     2 19741.13
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.49123    1.46753   1.016 0.309701    
## alpha   0.60068    0.06033   9.957  < 2e-16 ***
## A     312.74968   91.61362   3.414 0.000655 ***
## k     219.15324   28.08087   7.804 1.02e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6977 on 1752 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.964e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1752     852.89                         
## 2   1751     852.69  1  0.204  0.4189 0.5176
##   model      AIC
## 1     2 19741.13
## 2    2a 19742.70
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.49123    1.46753   1.016 0.309701    
## alpha   0.60068    0.06033   9.957  < 2e-16 ***
## A     312.74968   91.61362   3.414 0.000655 ***
## k     219.15324   28.08087   7.804 1.02e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6977 on 1752 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.964e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1751     828.43                                
## 2   1750     790.40  1 38.027  84.194 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 19741.13
## 2     3 19692.03
## 3     4 19611.51
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     2.33449    1.85609   1.258  0.20865    
## alpha   0.57698    0.05622  10.263  < 2e-16 ***
## a      12.02383    3.70753   3.243  0.00120 ** 
## b      93.63274   28.58260   3.276  0.00107 ** 
## c     137.55008    7.17906  19.160  < 2e-16 ***
## d       1.09309    0.05382  20.312  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6721 on 1750 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    424     163.07                               
## 2    423     146.44  1  16.63  48.035 1.57e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4280.845
## 2     2 4236.917
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2772     0.6406   0.433  0.66539    
## alpha   0.8452     0.1103   7.661 1.27e-13 ***
## A      97.9714    18.4871   5.299 1.87e-07 ***
## k      53.0581    19.0692   2.782  0.00564 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 423 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.825e-06
##   (24 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 4236.917
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2772     0.6406   0.433  0.66539    
## alpha   0.8452     0.1103   7.661 1.27e-13 ***
## A      97.9714    18.4871   5.299 1.87e-07 ***
## k      53.0581    19.0692   2.782  0.00564 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 423 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.825e-06
##   (24 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Error in nls(f_3, data = G_M334, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_4, data = G_M334, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     2 4236.917
## 2     3       NA
## 3     4       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2772     0.6406   0.433  0.66539    
## alpha   0.8452     0.1103   7.661 1.27e-13 ***
## A      97.9714    18.4871   5.299 1.87e-07 ***
## k      53.0581    19.0692   2.782  0.00564 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 423 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.825e-06
##   (24 observations deleted due to missingness)

summary

  • simple log-normal model: does not fit
  • log-normal alpha model: does not fit

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    214     80.493                              
## 2    213     77.386  1 3.1072  8.5523 0.003824 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2156.928
## 2     2 2150.386
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5816     0.5385  -2.937 0.003677 ** 
## alpha   0.4666     0.1455   3.207 0.001550 ** 
## A     235.0957    65.5828   3.585 0.000418 ***
## k     112.0187    30.9615   3.618 0.000371 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6028 on 213 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.283e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    213     77.386                          
## 2    212     77.224  1 0.16244  0.4459  0.505
##   model      AIC
## 1     2 2150.386
## 2    2a 2151.930
## 3    2b 2152.190
## 4    2c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5816     0.5385  -2.937 0.003677 ** 
## alpha   0.4666     0.1455   3.207 0.001550 ** 
## A     235.0957    65.5828   3.585 0.000418 ***
## k     112.0187    30.9615   3.618 0.000371 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6028 on 213 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.283e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    212     76.519                             
## 2    211     72.714  1  3.805  11.041 0.00105 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 2150.386
## 2     3 2149.940
## 3     4 2140.872
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5408     0.5351  -2.880 0.004391 ** 
## alpha   0.5053     0.1373   3.681 0.000295 ***
## a      22.4320     6.3018   3.560 0.000459 ***
## b     115.3948    27.5776   4.184 4.20e-05 ***
## c     156.2468    22.9600   6.805 1.03e-10 ***
## d       1.0795     0.2035   5.305 2.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.587 on 211 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal alpha model: fits

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Ecoprovince Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 2b 4 4
212 Laurentian Mixed Forest 2b 4 4
221 Eastern Broadleaf Forest 2a 4 4
222 Midwest Broadleaf Forest 2a 4 4
223 Central Interior Broadleaf Forest 2b 4 4
231 Southeastern Mixed Forest 2a 2a 2a
232 Outer Coastal Plain Mixed Forest 2b 2b 2b
234 Lower Mississippi Riverine Forest 2 2 2
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 2a 2a 2a
255 Prairie Parkland (Subtropical) 2 4 4
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 2a 2a 2a
313 Colorado Plateau Semi-Desert 1 3 3
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe NA NA NA
332 Great Plains Steppe 2 2 2
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 2a 4 4
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 2c 4 4
M223 Ozark Broadleaf Forest Meadow 2a 2a 2a
M231 Ouachita Mixed Forest 2 2 2
M242 Cascade Mixed Forest 2b 4 4
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 2a 2a 2a
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2a 4 4
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 2a 4 4
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2c 4 4
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 2 4 4
M334 Black Hills Coniferous Forest 2 2 2
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 2 4 4

table by ecoprovince

Ecoprovince Ecoregion region n.obs n.plots tau tau.variance tau.2.5 tau.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6884 2879 0.8128805 0.0341550 0.4505946 1.1751665 0.8315403 0.0007698 0.7771511 0.8859295 267.35244 219.35952 315.3454 87.16041 63.848690 110.47212 31.22968 27.877587 34.58178 112.93234 102.35431 123.51038 123.6601 112.13157 135.18857 1.0673927 0.9722764 1.1625091
212 Laurentian Mixed Forest east 22685 9493 1.0710340 0.0114002 0.8617530 1.2803150 0.7732144 0.0006389 0.7236709 0.8227579 115.78050 108.52419 123.0368 40.57330 37.341870 43.80472 22.95843 21.324590 24.59227 67.52314 64.47797 70.56831 103.1003 98.85456 107.34606 1.0873191 1.0294815 1.1451566
221 Eastern Broadleaf Forest east 7307 3560 0.1986788 0.0127951 -0.0230617 0.4204193 0.8862948 0.0007294 0.8333532 0.9392364 297.82149 264.84583 330.7972 36.53118 21.221548 51.84081 46.50096 25.983421 67.01851 143.42164 118.24029 168.60298 119.2359 103.41338 135.05839 1.1069755 0.8700791 1.3438719
222 Midwest Broadleaf Forest east 5846 2589 1.0625381 0.0439447 0.6515814 1.4734947 0.8721285 0.0018779 0.7871746 0.9570824 194.67994 169.43512 219.9248 40.40127 26.686540 54.11599 19.41594 12.154770 26.67712 96.66094 86.10982 107.21207 101.2566 92.41588 110.09733 1.0247052 0.8850278 1.1643826
223 Central Interior Broadleaf Forest east 10006 3860 0.9546737 0.0122188 0.7379941 1.1713534 0.7913140 0.0007280 0.7384252 0.8442028 128.12523 118.95212 137.2983 32.43433 30.544669 34.32400 14.36005 -34.143582 62.86369 100.63809 50.20456 151.07162 118.7396 95.12609 142.35311 1.5526382 0.8475389 2.2577374
231 Southeastern Mixed Forest east 12844 5935 1.2963478 0.0145029 1.0602901 1.5324056 0.7183089 0.0004146 0.6783943 0.7582235 220.17657 207.14256 233.2106 42.72274 38.206364 47.23911 NA NA NA NA NA NA NA NA NA NA NA NA
232 Outer Coastal Plain Mixed Forest east 13167 6463 0.7915440 0.0179347 0.5290391 1.0540489 0.6700200 0.0005556 0.6238177 0.7162223 206.16286 187.32559 225.0001 41.26733 35.663943 46.87072 NA NA NA NA NA NA NA NA NA NA NA NA
234 Lower Mississippi Riverine Forest east 1344 759 0.5256142 0.1674543 -0.2771902 1.3284185 0.7999862 0.0033505 0.6864285 0.9135439 478.26877 317.43343 639.1041 153.20836 92.986251 213.43046 NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest west 85 85 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2290 903 0.4025611 0.0477957 -0.0261705 0.8312927 0.7155331 0.0048541 0.5789034 0.8521628 148.57344 128.51110 168.6358 5.24468 -5.375071 15.86443 NA NA NA NA NA NA NA NA NA NA NA NA
255 Prairie Parkland (Subtropical) east 714 318 -0.3313144 0.1933208 -1.1945585 0.5319296 0.5607660 0.0110571 0.3543162 0.7672159 317.92075 170.63777 465.2037 133.30362 65.298767 201.30848 11.80379 8.071868 15.53571 88.95895 68.86844 109.04946 58.2985 48.40726 68.18973 1.0552552 0.8693319 1.2411786
261 California Coastal Chaparral Forest and Shrub west 26 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest west 159 157 1.7516497 6.5664031 -3.3107992 6.8140987 0.8326216 0.0596171 0.3502495 1.3149937 15896.57299 -23729.49974 55522.6457 5997.12443 -9642.323051 21636.57192 NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert west 218 218 -1.4503531 0.3524055 -2.6205414 -0.2801648 NA NA NA NA 277.89641 59.74344 496.0494 159.09011 32.903856 285.27637 40.15842 16.002996 64.31384 148.91133 71.48995 226.33270 142.7671 125.62629 159.90790 0.6409271 0.4552203 0.8266338
315 Southwest Plateau and Plains Dry Steppe and Shrub west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe west 232 128 0.4762293 2.5216695 -2.6547219 3.6071806 0.6443436 0.0858053 0.0667941 1.2218931 502.59644 -693.17910 1698.3720 360.75928 -562.768438 1284.28699 NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6778 3008 0.7210269 0.0260032 0.4049164 1.0371373 0.8165966 0.0005035 0.7726088 0.8605844 311.62395 275.78961 347.4583 106.27770 86.667211 125.88819 11.86910 6.238289 17.49991 156.98730 135.68083 178.29377 207.6905 155.55597 259.82507 1.7226645 1.5001895 1.9451395
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8186 3765 0.9934830 0.0154443 0.7498705 1.2370956 0.8984551 0.0011323 0.8324930 0.9644173 154.79938 145.99431 163.6045 44.43699 39.737017 49.13696 49.42999 24.556832 74.30314 102.10729 77.35940 126.85518 100.6116 94.35973 106.86354 1.1053708 0.8527202 1.3580215
M223 Ozark Broadleaf Forest Meadow east 893 348 0.0477424 0.0685395 -0.4660799 0.5615648 0.9033564 0.0052962 0.7605248 1.0461880 225.89814 176.32294 275.4733 51.43265 27.365362 75.49995 NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 1009 496 0.4620608 0.1889160 -0.3909092 1.3150308 0.7762262 0.0070908 0.6109745 0.9414779 306.46634 204.28218 408.6505 133.47106 82.495978 184.44613 NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest west 3303 3286 0.5900829 0.4555005 -0.7331980 1.9133639 1.0753087 0.0048303 0.9390411 1.2115764 536.31143 366.60451 706.0184 119.02407 98.879928 139.16821 0.00000 -10.616952 10.61695 467.63578 316.19522 619.07633 581.4147 381.08599 781.74336 2.0957100 1.8323621 2.3590578
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow west 1993 1828 7.8784574 19.1671377 -0.7075676 16.4644824 0.6235532 0.0122832 0.4061984 0.8409080 130.60786 34.85927 226.3564 90.96584 55.156230 126.77545 NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow west 367 367 -1.8270607 0.1225249 -2.4835133 -1.1706081 0.5964045 0.0165444 0.3341790 0.8586300 1027.37948 -762.41454 2817.1735 568.28926 -653.279611 1789.85813 42.68917 20.960445 64.41789 180.73752 99.98778 261.48725 177.7659 97.36014 258.17169 0.9807269 0.5729790 1.3884749
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow west 1757 1757 -0.8741218 0.1175653 -1.5466199 -0.2016237 0.5987195 0.0017710 0.5161802 0.6812588 313.50459 215.07174 411.9375 179.34693 109.621788 249.07207 27.03865 18.812107 35.26519 136.75568 101.23088 172.28048 241.1734 170.72545 311.62137 1.4840181 1.2113066 1.7567296
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 2621 2611 0.8489972 0.7218949 -0.8170458 2.5150402 0.4568543 0.0029828 0.3497617 0.5639469 133.15226 80.60113 185.7034 75.15432 60.404252 89.90438 11.69323 6.863029 16.52342 104.61495 64.72005 144.50985 258.3093 184.74038 331.87824 1.6565189 1.4121862 1.9008515
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow west 1758 1747 2.3344926 3.4450582 -1.3058885 5.9748736 0.5769754 0.0031608 0.4667081 0.6872428 312.74968 133.06615 492.4332 219.15324 164.077704 274.22878 12.02383 4.752172 19.29549 93.63274 37.57311 149.69237 137.5501 123.46966 151.63051 1.0930900 0.9875411 1.1986390
M334 Black Hills Coniferous Forest west 451 179 0.2772480 0.4103689 -0.9819086 1.5364046 0.8451811 0.0121699 0.6283424 1.0620199 97.97135 61.63333 134.3094 53.05812 15.576023 90.54022 NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow west 220 220 -1.5407977 0.2862822 -2.5955330 -0.4860625 0.5053432 0.0211720 0.2347287 0.7759577 235.09566 105.82124 364.3701 112.01875 50.988548 173.04894 22.43196 10.009441 34.85447 115.39477 61.03188 169.75766 156.2468 110.98635 201.50728 1.0795052 0.6783650 1.4806453

parameter variance co-variance

##                tau         alpha           a            b            c
## tau    0.034154968 -3.293976e-05 -0.17390829 -0.793823844 -0.079889622
## alpha -0.006423996  7.697974e-04  0.00263179  0.005057415 -0.002472449
## a     -0.550302776  5.547168e-02  2.92403993  1.052106639 -3.656498436
## b     -0.796006558  3.378001e-02  0.11402171 29.117970738 18.900890109
## c     -0.073504706 -1.515273e-02 -0.36360133  0.595598266 34.585699132
## d     -0.085697703  3.471544e-03 -0.56240022  0.570005584  0.910961614
##                   d
## tau   -7.684697e-04
## alpha  4.673493e-06
## a     -4.666248e-02
## b      1.492417e-01
## c      2.599435e-01
## d      2.354297e-03
##               tau         alpha             a            b            c
## tau    0.01140025  0.0004251389 -0.0437925935 -0.131046828 -0.025538513
## alpha  0.15752878  0.0006388922 -0.0002584548 -0.002546829 -0.001535693
## a     -0.49204748 -0.0122668871  0.6948210451 -0.011936079 -0.551432166
## b     -0.79000659 -0.0648555853 -0.0092169364  2.413666428  1.726771735
## c     -0.11042226 -0.0280484538 -0.3054033536  0.513114744  4.692060723
## d     -0.02407672 -0.0069386385 -0.6657573057  0.464024636  0.811153380
##                   d
## tau   -7.585637e-05
## alpha -5.175181e-06
## a     -1.637533e-02
## b      2.127243e-02
## c      5.184684e-02
## d      8.707130e-04
##               tau         alpha             a             b             c
## tau    0.01279505  0.0001236697 -1.710918e-01 -3.834621e-01  -0.027801875
## alpha  0.04048267  0.0007293676  7.656677e-04  5.272259e-04  -0.001632104
## a     -0.14451297  0.0027087298  1.095476e+02 -1.189418e+02 -59.265887462
## b     -0.26390421  0.0015197371 -8.846638e-01  1.650099e+02  85.926507053
## c     -0.03045101 -0.0074872641 -7.015394e-01  8.287447e-01  65.148239726
## d      0.02789528  0.0075874415 -9.289982e-01  9.309494e-01   0.901522674
##                   d
## tau    3.813172e-04
## alpha  2.476299e-05
## a     -1.175035e+00
## b      1.445159e+00
## c      8.793516e-01
## d      1.460391e-02
##               tau         alpha            a             b            c
## tau    0.04394466  0.0015084853 -0.179346620  -0.694574424 -0.027812045
## alpha  0.16605333  0.0018779363 -0.004808419  -0.009751327 -0.006264714
## a     -0.23098100 -0.0299569781 13.719166707 -10.991568329 -9.067076591
## b     -0.61561600 -0.0418087783 -0.551365984  28.967542723 15.126501182
## c     -0.02941947 -0.0320564803 -0.542823246   0.623214684 20.337143839
## d      0.04421864 -0.0008452601 -0.865739099   0.679738516  0.852702873
##                   d
## tau    6.604526e-04
## alpha -2.609841e-06
## a     -2.284726e-01
## b      2.606639e-01
## c      2.739844e-01
## d      5.076523e-03
##               tau         alpha            a             b             c
## tau    0.01221880  0.0005246004  -0.17767176 -6.604723e-02  2.095623e-02
## alpha  0.17589552  0.0007279794  -0.01386273  9.500917e-03  2.994822e-03
## a     -0.06495815 -0.0207643759 612.26706998 -6.327252e+02 -2.304800e+02
## b     -0.02322334  0.0136864379  -0.99386905  6.619590e+02  2.509666e+02
## c      0.01573773  0.0092141415  -0.77322540  8.097366e-01  1.451153e+02
## d      0.05479186  0.0187823639  -0.97922104  9.843806e-01  8.797111e-01
##                   d
## tau    0.0021785960
## alpha  0.0001822872
## a     -8.7156057856
## b      9.1101387099
## c      3.8119141288
## d      0.1293876360
##               tau         alpha            A            k             p
## tau    0.01450285  0.0001949633 -0.556054599 -0.003391909  1.483923e-05
## alpha  0.07950344  0.0004146487 -0.002302665 -0.001079011 -1.496585e-06
## A     -0.69439093 -0.0170060718 44.215374190 10.766491368  3.104088e-02
## k     -0.01222416 -0.0229978476  0.702731089  5.308804758  1.667267e-02
## p      0.01623981 -0.0096862943  0.615239101  0.953681138  5.757142e-05
##               tau         alpha            A            k             s
## tau    0.01793470  0.0001487194 -0.714972319 -0.006000287 -1.252955e-04
## alpha  0.04711369  0.0005555804  0.001985514 -0.001042707 -6.050837e-06
## A     -0.55553898  0.0087654029 92.353919166 22.803429480 -2.345681e-01
## k     -0.01567346 -0.0154749304  0.830065323  8.171851420 -8.801539e-02
## s     -0.02849401 -0.0078182057 -0.743372435 -0.937699133  1.078127e-03
##                tau        alpha            A             k
## tau    0.167454328  0.001355136  -17.1873405   -0.07518848
## alpha  0.057211002  0.003350503   -0.1997146   -0.10347624
## A     -0.512319070 -0.042085718 6721.0935598 2157.77792059
## k     -0.005985614 -0.058235955    0.8574175  942.29920519
##               tau        alpha           A           k            p
## tau    0.04779568  0.003696598  -1.5199537 -0.16251893 -0.106163461
## alpha  0.24269117  0.004854091  -0.0675872 -0.01053084 -0.006856526
## A     -0.67958786 -0.094824393 104.6600399 42.91056877 28.320759668
## k     -0.13727343 -0.027911676   0.7745522 29.32555886 19.521808318
## p     -0.13466118 -0.027290521   0.7676727  0.99967431 13.003993123
##               tau        alpha            a            b           c
## tau    0.19332077  0.007344857 -0.498615073  -4.19255053 -0.06671220
## alpha  0.15886342  0.011057077  0.000975675  -0.03706817 -0.02010617
## a     -0.59660668  0.004881429  3.613067354   9.03537112 -1.87751391
## b     -0.93184237 -0.034449620  0.464527443 104.71121089  8.74377683
## c     -0.03011686 -0.037953596 -0.196059915   0.16960793 25.38122913
## d     -0.03198883 -0.064081241 -0.427313399   0.11886019  0.83381407
##                   d
## tau   -0.0013319170
## alpha -0.0006381029
## a     -0.0769173197
## b      0.1151788166
## c      0.3978003365
## d      0.0089676615
##              tau       alpha             A             k             p
## tau    6.5664031  0.07181837 -1.285430e+04  2.219144e+03 -6.258973e-04
## alpha  0.1147854  0.05961707  3.499880e+02  2.097498e+02 -3.616051e-05
## A     -0.2500923  0.07146340  4.023169e+08  1.482250e+08 -4.322236e+01
## k      0.1093949  0.10851548  9.334968e-01  6.266846e+07 -1.793040e+01
## p     -0.1011995 -0.06136043 -8.928191e-01 -9.384361e-01  5.825345e-06
##            tau           a             b           c            d
## tau  0.3524055  -5.7246279  -22.06300480   0.5913954  0.001058122
## a   -0.7869475 150.1621212  309.82373329 -14.2180384 -0.299473936
## b   -0.9462740   0.6437364 1542.59841013 -15.3030414 -0.164524650
## c    0.1145671  -0.1334329   -0.04480790  75.6124585  0.544092506
## d    0.0189200  -0.2594093   -0.04446428   0.6641754  0.008875373
##              tau       alpha             A             k
## tau    2.5216695 0.069998493 -3.814150e+02   -109.227617
## alpha  0.1504831 0.085805282  4.572344e-01      3.437316
## A     -0.3960375 0.002573738  3.678196e+05 274225.961775
## k     -0.1468489 0.025052135  9.653247e-01 219399.393626
##               tau         alpha            a             b            c
## tau    0.02600316 -2.761285e-05 -0.034764631  -0.873034738  -0.07981265
## alpha -0.00763118  5.035155e-04  0.002764817  -0.003385973  -0.03071582
## a     -0.07505497  4.289581e-02  8.250688464 -19.708703824 -54.50843225
## b     -0.49811855 -1.388326e-02 -0.631287579 118.133058667 249.18479349
## c     -0.01861053 -5.147020e-02 -0.713540632   0.862056883 707.29367745
## d     -0.01897962 -4.291364e-02 -0.868218914   0.838638992   0.95816406
##                   d
## tau   -0.0003473411
## alpha -0.0001092842
## a     -0.2830283113
## b      1.0344662314
## c      2.8919801589
## d      0.0128798583
##               tau         alpha             a             b             c
## tau    0.01544427  0.0002536698  -0.196584244 -2.457777e-01  -0.033877302
## alpha  0.06066054  0.0011322901   0.000362471  1.665029e-03  -0.001163569
## a     -0.12466659  0.0008489447 161.001490491 -1.533477e+02 -18.532972265
## b     -0.15665222  0.0039194092  -0.957282318  1.593839e+02  20.752286053
## c     -0.08547293 -0.0108421847  -0.457966364  5.154032e-01  10.171689408
## d      0.02572335  0.0068963954  -0.951579959  9.424641e-01   0.667187808
##                   d
## tau    4.120174e-04
## alpha  2.990925e-05
## a     -1.556198e+00
## b      1.533528e+00
## c      2.742516e-01
## d      1.661150e-02
##               tau        alpha            A            k             p
## tau    0.06853953  0.000325955  -4.03057365  -0.27242629 -8.957156e-04
## alpha  0.01710824  0.005296189   0.05919583  -0.01203524 -4.468643e-05
## A     -0.60950072  0.032202330 638.03446216 254.39202464  8.047295e-01
## k     -0.08485817 -0.013486158   0.82129016 150.37291073  5.087456e-01
## p     -0.07711058 -0.013839115   0.71802949   0.93504024  1.968662e-03
##                tau         alpha            A            k
## tau    0.188915964  0.0001524564  -13.7273187   -0.7699364
## alpha  0.004165477  0.0070907629   -0.2150236   -0.2291201
## A     -0.606550870 -0.0490405568 2711.2422008 1121.5829707
## k     -0.068196498 -0.1047510125    0.8292563  674.7096641
##                tau         alpha            a             b             c
## tau    0.455500485  0.0003265189 -0.069700462  -47.94614555     0.1435947
## alpha  0.006961115  0.0048302571 -0.001789894    0.09259516    -0.1525302
## a     -0.019072122 -0.0047560897 29.321381165  -77.65294702  -327.1580595
## b     -0.919760452  0.0172491868 -0.185665489 5965.80551129  2889.1880122
## c      0.002082373 -0.0214800434 -0.591330013    0.36610509 10439.2904028
## d      0.020769211 -0.0133973082 -0.787866075    0.30434551     0.9421937
##                   d
## tau    0.0018827235
## alpha -0.0001250618
## a     -0.5730159677
## b      3.1573560191
## c     12.9299789035
## d      0.0180403195
##                 tau       alpha            A            k             p
## tau   19.1671377313  0.07485946 -209.0074296  -0.74797970 -8.433607e-05
## alpha  0.1542809916  0.01228319   -0.7054270  -0.04442519 -9.261757e-05
## A     -0.9778319433 -0.13036996 2383.6239698 181.85591933  2.626134e-01
## k     -0.0093567522 -0.02195268    0.2039964 333.40499318  6.009473e-01
## p     -0.0005107549 -0.02215724    0.1426185   0.87262612  1.422474e-03
##                tau        alpha             a            b            c
## tau    0.111425743 0.0002768889 -2.529440e+00  -10.4807058   -1.5065987
## alpha  0.006448933 0.0165443521  1.988780e-01    0.3286231    0.3070966
## a     -0.685816618 0.1399388646  1.220807e+02  172.2963033   -0.3624131
## b     -0.764658023 0.0622218146  3.797711e-01 1686.0134031 1062.0122181
## c     -0.110389609 0.0583947139 -8.022387e-04    0.6325901 1671.6804443
## d     -0.096351180 0.0339530989 -1.484090e-01    0.5268294    0.9183837
##                   d
## tau   -0.0066685434
## alpha  0.0009054938
## a     -0.3399891459
## b      4.4851989129
## c      7.7854190641
## d      0.0429894959
##                tau        alpha           a            b             c
## tau    0.117565294 -0.000447291 -1.08948293  -5.45404960    0.02726223
## alpha -0.030998552  0.001770999  0.02985268   0.03820798   -0.02760001
## a     -0.757556422  0.169125171 17.59267006  38.15338208  -45.61992825
## b     -0.878212045  0.050126191  0.50221194 328.06526847  280.79535627
## c      0.002213630 -0.018259256 -0.30281113   0.43161140 1290.13088760
## d      0.009871542 -0.034677596 -0.44745292   0.37590998    0.92231721
##                   d
## tau    0.0004706267
## alpha -0.0002029131
## a     -0.2609547462
## b      0.9467078193
## c      4.6062677563
## d      0.0193332096
##               tau        alpha           a            b            c
## tau    0.72189485  0.001706874 -1.81860986 -16.50260979   -2.5940486
## alpha  0.03678362  0.002982773  0.01413437  -0.01779304   -0.1041115
## a     -0.86893434  0.105063237  6.06779937  38.53960620  -15.6004142
## b     -0.95465737 -0.016012970  0.76899504 413.93891216  265.7892705
## c     -0.08137592 -0.050809308 -0.16880111   0.34819626 1407.6361975
## d     -0.05324810 -0.094018080 -0.30457223   0.27345268    0.9094210
##                   d
## tau   -0.0056373301
## alpha -0.0006398141
## a     -0.0934842063
## b      0.6932384732
## c      4.2515034037
## d      0.0155261823
##               tau        alpha            a            b           c
## tau    3.44505817  0.003520774 -6.729276173 -52.81352651 -0.15008650
## alpha  0.03373972  0.003160798  0.008731308  -0.02811251 -0.01063845
## a     -0.97787912  0.041888617 13.745792939 102.87060477 -0.82618681
## b     -0.99550903 -0.017494420  0.970743994 816.96483683 12.38096064
## c     -0.01126357 -0.026358017 -0.031040308   0.06033722 51.53884559
## d     -0.02568570 -0.098885667 -0.076109778   0.04570799  0.80089205
##                   d
## tau   -0.0025656358
## alpha -0.0002991831
## a     -0.0151855555
## b      0.0703070926
## c      0.3094187709
## d      0.0028960807
##               tau        alpha            A            k
## tau    0.41036895  0.008872732  -7.84008531  -0.31934954
## alpha  0.12555261  0.012169947  -0.03070134   0.07153567
## A     -0.66201025 -0.015053731 341.77292767 264.57032727
## k     -0.02614253  0.034005321   0.75048304 363.63262478
##               tau       alpha           a             b           c
## tau    0.28628223 -0.01338815 -2.83343963 -13.916816713  -0.8430314
## alpha -0.18227141  0.01884558  0.23803779   0.987256814   0.1778299
## a     -0.84033709  0.27515529 39.71243136 130.831786659  -5.8229042
## b     -0.94316230  0.26077686  0.75282452 760.523358217 139.7773938
## c     -0.06862364  0.05641925 -0.04024423   0.220753656 527.1637135
## d      0.04196025  0.06218896 -0.25485915   0.006191206   0.7517345
##                  d
## tau    0.004568621
## alpha  0.001737272
## a     -0.326823523
## b      0.034744122
## c      3.512263217
## d      0.041409469

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plot k (stand age at half biomass asymptote)

## Warning: Removed 12 rows containing missing values (`geom_point()`).